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A239362
Decimal expansion of Sum_{k>=1} 1/((3k-2)*(3k-1)*(3k)).
2
1, 7, 8, 7, 9, 6, 7, 6, 8, 8, 9, 1, 5, 2, 7, 0, 3, 9, 7, 9, 9, 7, 0, 8, 2, 5, 5, 1, 7, 9, 9, 0, 7, 5, 0, 6, 9, 0, 9, 1, 4, 3, 9, 2, 2, 5, 6, 7, 4, 9, 7, 7, 8, 0, 9, 5, 8, 7, 9, 7, 6, 5, 0, 4, 3, 7, 6, 5, 7, 2, 2, 1, 9, 7, 6, 9, 3, 6, 2, 2, 9, 2, 0, 2, 6, 2, 7
OFFSET
0,2
REFERENCES
L. B. W. Jolley, Summation of series, Dover Publications Inc. (New York), 1961, p. 46 (series n. 250).
LINKS
Anthony Sofo, Euler related binomial sums, Indian J. Pure Appl. Math. 50 (1) (2019) 149-160, S(3).
FORMULA
Equals ( Pi*sqrt(3)/3 - log(3) )/4.
EXAMPLE
0.1787967688915270397997082551799075069091439225674977809587976504...
1/(1*2*3) + 1/(4*5*6) + 1/(7*8*9) + 1/(10*11*12) + 1/(13*14*15) + ...
MAPLE
evalf[100]((Pi*sqrt(3) - 3*log(3))/12 ); # G. C. Greubel, Aug 11 2019
MATHEMATICA
RealDigits[(Pi Sqrt[3]/3 - Log[3])/4, 10, 100][[1]]
PROG
(PARI) default(realprecision, 100); (Pi*sqrt(3) - 3*log(3))/12 \\ G. C. Greubel, Aug 11 2019
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (Pi(R)*Sqrt(3) - 3*Log(3))/12; // G. C. Greubel, Aug 11 2019
(Sage) numerical_approx((pi*sqrt(3) - 3*log(3))/12, digits=100) # G. C. Greubel, Aug 11 2019
CROSSREFS
Cf. A164833: Sum_{k>=1} 1/((4k-2)*(4k-1)*(4k)).
Sequence in context: A010728 A291509 A153856 * A094819 A019861 A065470
KEYWORD
nonn,cons
AUTHOR
Bruno Berselli, Mar 17 2014
STATUS
approved